An extension of the linear Luikov system equations of heat and mass transfer

Silva, Fernanda R. G. B.; Gonçalves, Giane; Lenzi, Marcelo Kaminski; Lenzi, E. K.

doi:10.1016/j.ijheatmasstransfer.2013.04.007

Cited by 15 publications

(11 citation statements)

References 42 publications

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“…corresponds to the well-known Riemann-Liouville fractional operator [41] for 0 < 1(2) < 1, which has been applied in several situations related to anomalous diffusion [42][43][44][45]. The exponential kernel…”

Section: Diffusion and Surface Effectsmentioning

confidence: 99%

Diffusion Process and Reaction on a Surface

Fuziki

Lenzi

Ribeiro

et al. 2018

Advances in Mathematical Physics

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We investigate the influence of the surface effects on a diffusive process by considering that the particles may be sorbed or desorbed or undergo a reaction process on the surface with the production of a different substance. Our analysis considers a semi-infinite medium, where the particles may diffuse in contact with a surface with active sites. For the surface effects, we consider integrodifferential boundary conditions coupled with a kinetic equation which takes non-Debye relation process into account, allowing the analysis of a broad class of processes. We also consider the presence of the fractional derivatives in the bulk equations. In this scenario, we obtain solutions for the particles in the bulk and on the surface.

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Section: Diffusion and Surface Effectsmentioning

confidence: 99%

Diffusion Process and Reaction on a Surface

Fuziki

Lenzi

Ribeiro

et al. 2018

Advances in Mathematical Physics

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“…Andarwa and Tabrizi [30] studied non-Fourier heat transfer effects on the heat and mass transfer coupling based on the Luikov's model. Silva et al [31] extended the classical Luikov's model to a more generalized form to describe the non-Markovian process of the coupled heat and mass transfer through the porous media. To investigate the influence of fracture-matrix interactions on the anomalous heat transfer in geological sites, Suzuki et al [32] extended a fractional heat transfer equation to characterize anomalous thermal diffusion in a fractured reservoir.…”

Section: Introductionmentioning

confidence: 99%

Transient response of hygrothermoelastic field in an elastic plate with an edge crack

Zhang

2020

Z Angew Math Mech

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In order to describe the complex interaction in the heat and moisture transfer process, a coupled time‐fractional hygrothermal theory is developed to describe the anomalous phenomenon of coupled heat and moisture diffusion. The hygrothermoelastic behaviors in a plate with an edge crack are investigated. The surfaces of the plate are both subjected to hygrothermal shocks. The Laplace transform and the finite Fourier transform are applied to seek an analytical solution of temperature change, moisture distribution, and stress response that are expressed in terms of the Mittag‐Leffler function. With this solution, the stress intensity factors at the crack tip are numerically calculated through the weight function method. The coupling effects of the heat and moisture on the stress intensity factors are illustrated graphically for sub‐diffusion, normal diffusion, and super‐diffusion respectively. The results show that the coupling hygrothermal effects are significant and different when compared with the uncoupled model.

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“…By now quite a large number of [22][23][24][25] models of the process dehydration of highlywatered porous particles have been designed. However, most of them are based on some assumptions, which can significantly simplify the procedure of modeling.…”

Section: Introductionmentioning

confidence: 99%

“…However, most of them are based on some assumptions, which can significantly simplify the procedure of modeling. For example, the temperature equilibrium [22] on the partition border of the system "water-vapor" or application method of moisture-potential [23]. Models of [24,25] "drying" of wet timber are based on the concept of volume phase transition of the distribution in space.…”

Section: Introductionmentioning

confidence: 99%